Knot removal for parametric B-spline curves and surfaces
Computer Aided Geometric Design
Automatic fairing algorithm for B-spline curves
Computer-Aided Design
Progress in computer graphics (vol. 1)
Geometric concepts for geometric design
Geometric concepts for geometric design
Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
The NURBS book
Interpolating curve with B-spline curvature function
Proceedings of the international conference on Mathematical methods for curves and surfaces II Lillehammer, 1997
A method for determining knots in parametric curve interpolation
Computer Aided Geometric Design
A New Method of Interpolation and Smooth Curve Fitting Based on Local Procedures
Journal of the ACM (JACM)
Geometric modeling with splines: an introduction
Geometric modeling with splines: an introduction
Applied Geometry for Computer Graphics
Applied Geometry for Computer Graphics
Curvature and the Fairness of Curves and Surfaces
IEEE Computer Graphics and Applications
Target curvature driven fairing algorithm for planar cubic B-spline curves
Computer Aided Geometric Design
Practical Linear Algebra: A Geometry Toolbox
Practical Linear Algebra: A Geometry Toolbox
NURBS curve shape modification and fairness evaluation for computer aided aesthetic design
ISCGAV'07 Proceedings of the 7th WSEAS International Conference on Signal Processing, Computational Geometry & Artificial Vision
NURBS curve shape modification and fairness evaluation
WSEAS Transactions on Computers
Adaptive moving least squares for scattering points fitting
WSEAS Transactions on Computers
The theory and application of an adaptive moving least squares for non-uniform samples
WSEAS Transactions on Computers
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A method to generate a quintic B-spline curve which passes through the given points is described. In this case, there are four more equations than there are control point positions. Therefore, four gradients which are the first derivative of a quintic B-spline equation are assigned to the given points. In addition to this method, another method to generate a quintic B-spline curve which passes through the given points, and which has the first derivative at these given points is described. In this case, a linear system will be underdetermined, determined or overdetermined depending on the number of given points with gradients. A method to modify a quintic B-spline curve shape according to the specified radius of curvature distribution to realize an aesthetically pleasing freeform curve is described. The differences between the B-spline curve radius of curvature and the specified radius of curvature is minimized by introducing the least-squares method.